Dawson kicked three field goals of 50-yards or more in the game, connecting from 51-yards in the third quarter and then 50- and 52-yards in the the fourth quarter.
Baltimore led the entire game. The Ravens scored in the first quarter on an 18-yard pass from Joe Flacco to Torrey Smith. They botched the point-after attempt, but got a field goal later in the quarter to go up 9-0.
Cleveland cut the lead to 9-7 in the second quarter on a 1-yard touchdown run by Trent Richardson. Richardson finished with 47 yards on 14 carries. He also caught 4 passes for 57 yards.
Baltimore scored two touchdowns in the third quarter, sandwiched around a Dawson field goal. Flacco scored on a 1-yard run early in the quarter, then Cary Williams intercepted a Brandon Weeden pass and returned it 63 yards for a touchdown just before the third quarter ended to put Baltimore up 23-10.
Dawson's two field goals brought the Browns within a touchdown. Cleveland got the ball back with 1:05 remaining and drove to the Baltimore 18, but couldn't get it into the end zone on their final play.
Weeden finished 25-for-52 for 320 yards, no touchdowns and an interception. Greg Little caught 4 passes for 77 yards. Cleveland's defense had four sacks and an interception in the game.
Flacco completed 28-for-46 passes for 356 yards with a touchdown and an interception. Ray Rice had 18 carries for 49 yards. Anquan Boldin caught 9 passes for 131 yards.
Cleveland falls to 0-4 while the Ravens improved to 3-1.